Theorem hbn1 1698

Description: x is not free in -. A. x ph. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 18-Aug-2014.)

Assertion

Ref	Expression
hbn1	|- ( -. A. x ph -> A. x -. A. x ph )

Proof of Theorem hbn1

Step	Hyp	Ref	Expression
1		ax6b 1697	1 |- ( -. A. x ph -> A. x -. A. x ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1393

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 617  ax-in2 618  ax-5 1493  ax-gen 1495  ax-ie2 1540  ax-ial 1580

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-fal 1401

This theorem is referenced by:  modal-5  1706  dvelimfALT2  1863